Extended cutting-plane method

Westerlund, T. H. Skrifvars I. Harjunkoski, and R. Pom. An Extended Cutting Plane Method for a Class of Non-convex MINLP Problems. Comput Chem Eng 22 357-365 (1998). 

Westerliind, T. and Lundqvist, K. (2003) Alpha-ECP, Version 5.04. An interactive MINLP-solver based on the extended cutting plane method Report 01-178-A, Process Design Laboratory, Abo Akademi University Abo, Finlande. 

To solve the problem above the branch and bound method (see e.g. [106]), generalized Benders Decomposition [108], Outer Approximation [109, 110], LP/NLP branch and bound [111] and Extended Cutting Plane Method [112] are in use. Grossmann and Kravanja [113] give an extensive compilation of literature on MINLP problems. 

The methods discussed in this section can be extended to systems that have more than three components. The problem is to convert each system to a pseudobinary system. For a quaternary system, the properties of an equilateral tetrahedron may be used to depict the composition of the system. The composition axes would be four lines drawn from the four apexes perpendicular to the opposite faces. Planes cutting the tetrahedron parallel to the bases would represent pseudoternary systems for which one composition variable would be constant. Pseudobinary systems would be depicted by the intersections of two of the pseudoternary planes. Indeed, the experimental measurements and calculations would be extensive. 

Figure 2.10 Cylindrically symmetric hydrodynamical model of accretion flow with rotation during the early collapse phase, showing the inflow of matter in the meridional plane and the build-up of a flat rotating disk structure after about 1.05 free-fall times. Arrows indicate matter flow direction and velocity, gray lines indicate cuts of isodensity surfaces with meridional plane. Dark crosses outline locations of supersonic to subsonic transition of inflow velocity this corresponds to the position of the accretion shock. Matter falling along the polar axis and within the equatorial plane arrive within 1600 yr almost simultaneously, which results in an almost instantaneous formation of an extended initial accretion disk [new model calculation following the methods in Tscharnuter (1987), figure kindly contributed by W. M. Tscharnuter],...

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